The first RFR (Réseau Formation Recherche) lead 4 ALADINers to a PhD degree. Three out of the five students of the second RFR have already successfully defended. These PhD studies were mainly realized in Toulouse. The eighth defense will take place very soon.
Meanwhile, some PhD studies are going on without any specific funding as the PhD work is done mainly at home (in Belgium for Luc, in Morocco for Radi and Wafaa and in Toulouse for Jean-Marcel).
The incremental approach proposed by Courtier et al (1994) reduces the computation cost of the original 4D-Var algorithm. An approximate solution is found iteratively by solving several quadratic cost functions, approximations of the original one, obtained by the linearization of the model and the observation operators at lower spectral truncations. The solutions at low resolution are used as a correction to update the initial state at high resolution. The constant term of the linearization represents the model equivalent at observation points and is always computed at full resolution. In this way non-linearities are taken into account.
At low resolution, the tangent linear version of the model is used to transport the errors (instantaneous increments) along the assimilation period. This linearized version of the model must take into account not only the dynamics part, but the physics as well.
However, physical processes such as condensation, convection, vertical diffusion, …etc, are highly nonlinear and often discontinuous with frequent thresholds, which may cause serious convergence problems in the minimization. As a consequence, in the incremental 4D-Var framework, the errors (increments) are transported by a tangent linear model including a linearization of a regularized package of simplified physics. (Janiskova et al, 1997)
The operational 4D-Var at Météo-France uses a multiple-truncation incremental approach (Veerse and Thépaut, 1997) consisting in doing three minimizations at different truncations T42, T63 and T95; the forecast model being done at truncation T199 in stretched grid.
Some problems of unrealistic precipitation over Sahara area, which were already present in the 3D-Var ARPEGE version, are amplified with the 4D-Var implementation. The first part of this thesis tries to understand this problem in the framework of incremental 4D-Var.
Several 4D-Var assimilation cycles have been done over a period of 15 days (June 2000) with overestimated precipitations in the operational 4D-Var. The main results could be synthesized as it follows :
As a first conclusion, we can suppose that the multi-incremental approach has a bad impact over tropical areas. In the concept of this approach, a lot of combined factors are present and could explain this fact :
In order to be able to conclude about theses factors, a set of single observation analyses has been performed to compare the increments between a simple truncation incremental (T95, T95, T95) analysis and a multiple truncation incremental (T42, T63, T95) one.
A single observation of specific humidity injected at the beginning of the assimilation period in the middle of the Sahara zone causes different increments of specific humidity in term of shape and magnitude between the two analyses : the pattern is larger in multi-incremental analysis and the values are bigger. The impact of this observation on temperature and geopotential increments are still the same between the two experiments.
Other single observations of temperature and geopotential were injected separately at the same location, experiments which didn't create any big differences.
Now, similar experiments are being done by injecting single observations at the middle and the end of the assimilation period. The behavior of the total and partial cost functions (related to observations and first-guess), are also checked to make conclusions about the convergence of the two different approaches (simple incremental and multiple incremental).
The PhD defense will take place in Bucarest (Romania) on February 26th, 2001 and Doina promises us a nice final report for the next Newsletter.
Some parameterization hypotheses taken for the global model ARPEGE loose their validity with small mesh sizes and time steps, and should be refined to ensure a better behavior for mesh sizes below 10 km.
After presenting the ensemble of the physical parameterizations of the ALADIN model, our work focus on the deep convection scheme, which contained the more critical approximations. Before thinking of non-hydrostatic physics, several wants of the scheme had to be answered. A first packet came with the CYCORA/CYCORA-bis enhancements, from which we developed the horizontal momentum advection and the pressure gradient aspects, with the so-called 'Connex Active Layers' calculation. After this we felt the need to relax the hypothesis of quasi-equilibrium between the large scale forcing and the convective activity, which led us to relaunch developments around prognostic draught vertical velocity and mesh fraction. The availability of the prognostic mesh fraction gave us a chance to revisit another limitation, the negligible convective mesh fraction hypothesis. The prognostic scheme seems to give better results already with mesh sizes of 7 km. There still remain, in our view, particular topics that should be addressed. The highly needed introduction of prognostic suspended condensed phases is still under development by others. We could also mention the lack of a local mass budget for each layer, or the problems associated to some artificial separations, as the difficulty to link large scale and subgrid effects, or reciprocal influences between updraught and downdraught.
On the way to develop non-hydrostatic effects in the physical package, a first step was also done with the vertical turbulent diffusion of the two non-hydrostatic variables. These variables could also in the future play a part in other parameterizations, like the convection scheme.
The purpose is to investigate the methods used to validate the physical packages of NWP models. The aim is to improve the methods, in order to better point out the compensating errors between physical parameterizations. 3D and 1D model runs will be used, looking at results both from large scale and small scale points of view. Special attention will be paid on the life cycle of clouds, at these different scales.
Summary
This project of thesis aims at improving the knowledge of the assimilation systems based on variational approach. It is particularly a question to develop a set of diagnostics allowing to validate a posteriori any analysis and assimilation algorithm, by estimating the accuracy of the error statistics (observation, background) specified in entry of the assimilation system. Besides a detailed study of the adjoint solution can allow to reflect the errors affecting the assimilating model. The propose is to investigate objective methods to define the error statistics required by the assimilation.
This work splits into two main topics :
Results obtained
Only the study on the limited area model was so far approached. Some diagnostics have been tried in ALADIN, to adjust the "lagged-NMC" background error statistics computed using the NMC method. Such statistics allow to reduce the energy in the large-scale spectrum, and to have more mesoscale representative analysis increments. This problem is, in its simplest formation, equivalent in reassessing the relative weight of background and observation cost function by tuning the ratio "l=Jo/Jb".
In first method, scores with respect to the radiosonde observations are computed. They give an objective measure of the quality of the analysis. It consists in generating distance of background errors, between radiosonde observations located in the ALADIN domain, and forecast fields at 06 hour range. Thus, we can use the ALADIN error contribution, to calibrate the variances in the "lagged NMC" statistics. As result, this method seems to indicate that the parameter "l" that we try to calibrate in ALADIN must be close to 1.
A posteriori calibration used by Talagrand (1998) and Talagrand and Bouttier (1999), concerns the evaluation of the internal consistency of the background error statistics specified in entry of the assimilation system. According to this diagnostic, a variational system is called "consistent", if the statistical average of the cost function at its minimum is simply proportional to the number of observations.
The application to the 3D-Var in ALADIN produced similar results to those obtained by the ECMWF system : the innovation vector (difference between the most recent forecast and the new observations) is overestimated. However, the daily variability of the diagnostic, revealed in the limited area model, is more marked than in a global model. Concerning the tuning of the parameter "l", the first results suggest that such a tuning (aiming at a single parameter) is not sufficient.
On the other hand, in association with G. Desroziers (CNRM/GMME), a finer evaluation concerned both terms of cost function (background and observation term). The framework is given by an analysis problem with realistic data. The diagnostic uses a randomized method as required by the Generalized Cross Validation. The idea here is to simulate both background and observations variances that should give the best analysis. The results for the current ALADIN 3D-Var system, show an under-estimation of the background error variance, and an overestimation of the observation one.
The PhD study is mainly completed (see report in Newsletter 18). Now, Filip will put pen to paper and write his thesis.
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